From your screen shot, you haven't got avast free but a trial of the avast Internet Security, so your free registration key won't fit where it is expecting the license/activation for avast Internet Security.
How did you end up with the trial for avast 7 Internet Security ?
The only way to resolve this is to reinstall avast 7 free, if you can connect with avast 7 then you should be able to connect with avast 8. This may be down to your firewall blocking avast, but with win7 firewall outbound protection is disabled by default, so that shouldn't be the issue.
I would suggest a clean install of avast 8 free (or avast 7 if you find the free version):
- Download the latest version of avast, 8.0.1483
http://files.avast.com/iavs5x/avast_free_antivirus_setup.exe and save it to your HDD, somewhere you can find it again (if you didn't save your last download). Use that when you reinstall.
- Download the avast! Uninstall Utility, aswClear.exe
find it here and save it to your HDD (it has uninstall tools for all versions).
- 1. Now uninstall avast! - using add remove programs, if you can't do that (as appears to be the case) start from the next step, reboot.
- 2. run the avast! Uninstall Utility, it will request it be run from safe mode (and will handle the boot into safe mode), first for 7.x if previously installed and then for 8.0, once complete reboot into normal mode.
- 3. install the latest version, reboot.